Using Array modifier, is it possible to gradually increase the offset?
You can control the density of the sticks around the curve by using DupliFrames, and adjusting the 'speed' the stick 'travels' around the curve.

Starting with a curve and a stick, all origins at 0:
(Here, we're arranging 120 sticks)


Assign a 'Follow Path' constraint to the stick, with the curve as its path. Do not hit the 'Animate Path' button.
Set the stick's 'Duplication' method to 'Frames' with the Start at 1 and the End at 120.
Adjust the curve's 'Path Animation' > 'Frames' to 120.
Right-click, and insert keyframes on the constraint's 'Offset' field: 0 at frame 0, 120 at frame 120.
With that field active, open a graph editor window to see the F-curve of its animation.


You can now control the density of the sticks by altering the F-curve. I changed the end-keys (V) to 'Vector' type to begin with, to start with a straight line and even distribution. I then inserted 'Vector' keys at frames 30 and 90, converted them to 'Automatic', and rotated them a bit to get the distribution shown.

The illustration shows: The result from above, The F-Curve,  all the relevant panels, and the timeline.